## Math Problem Statement

A certain element has a half life of 4.5 billion years. a. You find a rock containing a mixture of the element and lead. You determine that 55% of the original element remains; the other 45% decayed into lead. How old is the rock? b. Analysis of another rock shows that it contains 20% of its original element; the other 80% decayed into lead. How old is the rock? Question content area bottom Part 1 a. The rock is approximately 3.9 billion years old. (Round to one decimal place as needed.) Part 2 b. The rock is approximately enter your response here billion years old. (Round to one decimal place as needed.)

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Exponential Decay

Half-Life

Logarithms

### Formulas

N(t) = N_0 * (1/2)^(t/T)

ln(N(t)/N_0) = (t/T) * ln(1/2)

### Theorems

Exponential Decay Formula

### Suitable Grade Level

High School (Grades 10-12)

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